0 votes
1.3k views
in Statistics by (27.3k points)
closed by

The following table shows the marks scored by 140 students in an examination of a certain paper:

 Marks:  0 - 10  10 - 20  20 - 30  30 - 40  40 - 50
 Number of students:  20  24  40  36  20

Calculate the average marks by using all the three methods: direct method, assumed mean deviation and shortcut method.

1 Answer

+1 vote
by (26.1k points)
selected by
 
Best answer

From Direct method:

 Class interval  Mid value (xi)  fi  fixi
 0 - 10  5  20  100
 10 - 20  15 24  360
 20 - 30  25 40 1000
 40 - 50  45  20  900
 
 N = 140 \(\sum\)fixi = 3620

Mean = \(\frac{\sum f_ix_i}{N}\)

\(=\frac{3620}{140}=25.857\)

Assumed mean method: 

let assumed mean (A) = 25

Mean = A + \(\frac{\sum f_iu_i}{N}\)

 Class interval  Mid value (xi)  ui = xi - A  fi  fiui
 0 - 10  5 -20 20 -400
 10 - 20 15 -10 24 -240
 20 - 30 25 0 40 0
 30 - 40 35 10 36 360
 40 - 50 45 20 20 400
 N = 140 \(\sum\)fiui = 120


Mean = A + \(\frac{\sum f_ix_i}{N}\)

\(=25+\frac{120}{140}=25+0.857\)

\(=25.857\)

Step deviation method: Let the assumed mean (A) = 25

 Class interval  Mid value (xi)  di = xi - A = xi - 25  ui\(\frac{xi-25}{10}\)  Frequency (fi)  fiui
 0 - 10 5 -20 -2 20 -40
 10 - 20 15 -10 -1 24 -24
 20 - 30 25 0 0 40 0
 30 - 40 35 10 1 36 36
 40 - 50 45 20 2 20  40
 N = 140 \(\sum\)fiui = 12


Mean = A + \(\frac{\sum f_iu_i}{N}\times h\)

\(=25+0.857=25.857\)

\(=25+\frac{12}{140}\times10\)

\(=25+0.857=25.857\)

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...